Free energy and emittance growth in nonstationary charged particle beams

Abstract

Charged particle beams that are not perfectly matched or centered when injected into a focusing channel (or accelerator) have a higher total transverse energy than the equivalent ideal stationary beam. The excess energy ΔE represents free energy that can cause emittance growth. A general relationship between the possible emittance growth and ΔE is derived, and analytical results are presented for nonuniform, mismatched, and off-centered beams.